Horizontal Hyperbolas Dynamic Demonstration

① This example demonstrates the geometric construction and key features of a horizontally oriented hyperbola, with standard equation (x-h)²/a² - (y-k)²/b² = 1. ② Core mathematical concepts include the center, vertices, foci, eccentricity, asymptotes, and symmetry of the hyperbola; it also touches on linear regression, inequalities, and hypergeometric distribution as extended tags, but the main focus is conic sections in analytic geometry. ③ Construction highlights: from the construction summary, parameters a, b, h, k define the size and center position; point C is the center; c computes the focal distance (c² = a² + b²); F1h and F2h are the two foci; V1 and V2 are vertices; e is eccentricity; boo1 and boo2 likely control display toggles; E is an auxiliary point; text1_1 is a text label; g and d may represent asymptotes or auxiliary lines. GeoGebra commands involve object definitions, geometric relation calculations, and dynamic text. ④ Suitable for high school or early college analytic geometry courses, this interactive tool helps students intuitively understand the definition, properties, and parameter effects of hyperbolas, and is useful for classroom demonstrations or self-directed exploration.